Metallocenes and their use as catalysts in the polymerization of olefins have been known for a long time (EP-A 129 368 and the literature cited therein). Furthermore, EP-A '368 discloses that metallocenes in combination with aluminum alkyl/water as cocatalysts are effective systems for the polymerization of ethylene. (Thus, for example, 1 mol of trimethylaluminum and 1 mol of water form methylaluminoxane=MAO. Other stoichiometric ratios have also been successfully employed (WO 94/20506).) Metallocenes whose cyclopentadienyl frameworks are covalently linked to one another by a bridge are also already known. As an example of the numerous patents and applications in this field, mention may be made of EP-A 704 461 in which the linking group mentioned is a (substituted) methylene or ethylene group, a silylene group, a substituted silylene group, a substituted germylene group or a substituted phosphine group. In EP '461 too, the bridged metallocenes are envisaged as polymerization catalysts for olefins. Despite the numerous patents and applications in this field, there is still a desire for improved catalysts which have a high activity so that the amount of catalyst remaining in the polymer can be made small and which are equally suitable for the polymerization and copolymerization of olefins to give thermoplastics and to give elastomeric products and for the polymerization and copolymerization of diolefins, if desired together with olefins.